To "pick out" something means to choose what you want. You use this phrase when talking about choosing from among a lot of different options. It's often used when shopping:

I picked out a nice dress for you to wear to Aiko's graduation.

You don't use the phrase "pick something out" when you have only 2 or 3 options.

It's also more casual to say "pick out" than to use the word "choose".